Manager Crowding and Portfolio Construction · ©2012. All rights reserved. msci.com msci.com Manager Crowding and Portfolio Construction Do Risk Models Cause Manager Crowding? Jyh-Huei

msci.com ©2012. All rights reserved. msci.com

Manager Crowding and Portfolio Construction Do Risk Models Cause Manager Crowding?

Jyh-Huei Lee, Oleg Ruban, Dan Stefek, Jay Yao

msci.com ©2012. All rights reserved.

Why Do Crowded Trades Cause Concern?

Given that we all use similar software and data, read the same academic journals and are on the same broker-research email lists,

is it any wonder that trades become crowded and outperformance is competed away?

FT Adviser; February 27, 2012

Following the 2007 “Quant Meltdown” investors became concerned about the link between quant strategies and crowded trades

Crowded trades relate to similarities in portfolio positions

The risk is that investors may all try to exit their positions at the same time (and in the same direction)

Liquidity problems as everyone’s rushing to exit a “burning house”

Portfolio positioning and awareness of crowded trades are increasingly important at times of uncertainty

2


What’s a Crowded Trade?

There is no universally accepted definition

Signs of crowding

Similar holdings

Correlation in returns

Crowding is thought to be caused by managers using similar:

Alpha signals

Portfolio construction methodologies and risk models

Risk policies and constraints

3


Crowded Trades and Risk Models

Quant managers often craft their own alphas, but use standard risk models purchased from vendors

Does using a standard risk model in portfolio optimization promote crowding among managers?

Does using a proprietary risk model avoid crowding?

Little analytical research on these issues

4


What Does It Mean To Be More Crowded?

Compare different ways of building portfolios

Position is proportional to alpha (naïve approach)

Rank stocks by alphas, long top quintile, short bottom quintile

Position is determined through mean-variance optimization

Does portfolio optimization result in more crowding

More correlated holdings?

More correlated returns?

5


Intuition

Optimized portfolios can be more or less correlated than naïve portfolios

If residual alpha is less correlated than alpha, optimized portfolios tend to be less correlated

If residual alpha is more correlated than alpha, optimized portfolios tend to be more correlated

6

Alpha =Spanned alpha

Residual alpha

Risk model factors

+


Interplay of Alpha and Risk Models in Optimization

Optimizer puts more weight on the residual alpha

More specifically,

7

R

R

Optimal portfolio exposures

R

X

AdjustmentRisk

FactorSpecific

Adjustment

RiskSpecifich R*


Case 1: Same Spanned Alpha, Different Residual Alpha

Both managers follow earnings-based strategies

One component of both managers’ alpha is Barra US Equity Model (USE4) earnings yield

Second component is different for each manager

Residual alphas have low correlations in exposure and return

8

Manager 1 alpha =

Earnings Yield

Accrual

+

USE4 factors

Manager 2 alpha

=

+

Earnings Momentum


Case 2: Same Residual Alpha, Different Spanned Alphas

Each manager bets on different USE4 factor

Both managers bet on accrual

Residual alphas are perfectly correlated (polar case!)

9

Manager 1 alpha = Momentum

+

USE4 factors

Manager 2 alpha =

Accrual

Earnings Yield


Does Using a Standard Risk Model Cause Crowding

10

In the first case optimizing with the same model differentiates managers

Residual alphas are distinct; this distinction is emphasized by the optimizer

In the second case optimizing promotes crowding

Residual alphas are the same; spanned alphas are different and negatively correlated

Holding and

forecast return

correlations

Naive Q1 - Q5

Optimized

long-short

with USE4S

Holding 0.51 0.47 0.20

Return 0.90 0.89 0.30

Holding 0.57 0.36 0.97

Return 0.56 0.46 0.90

Case 1

Case 2


Proprietary Risk Models

11

Proprietary (or custom) risk models include the manager’s alpha signals as risk factors

Two main objectives in creating these models:

Produce better risk forecasts

Achieve better alignment between the manager’s alpha and the optimized portfolio

Does using a proprietary risk model in optimization help differentiate a manager from others?


Do Proprietary Models Reduce Crowding?

12

Proprietary model associates risk with the residual alpha

In the first case, using a proprietary models creates more overlap relative to a standard model

In the second case, using a risk model that includes the residual alpha leads to less crowding

USE4SProprietary

model

Case 1 0.51 0.46 0.12 0.24

Case 2 0.49 0.28 0.96 0.88

Optimized long-short

Naive Q1 - Q5

January 2002-December 2009

Average Holding Correlations


How Robust Are These Findings?

13

-0.20

0.00

0.20

0.40

0.60

0.80

1.00

Ho

ldin

gs c

orr

ela

tio

n

Naive Q1-Q5 USE4S Proprietary model

Case 1: same spanned alpha, different residual alpha


-0.2

0

0.2

0.4

0.6

0.8

1

Ho

ldin

gs c

orr

ela

tio

n

Naive Q1-Q5 USE4S Proprietary model

How Robust Are These Findings?

14

Case 2: different spanned alpha, same residual alpha


The Impact of Constraints

15

Case 1: same spanned alpha, different residual alpha

Case 2: same residual alpha, different spanned alphas

Tracking error USE4SProprietary

model

1% 0.19 0.27

3% 0.23 0.28

5% 0.21 0.24

Average holding correlations: January 2002-December 2009

Tracking error USE4SProprietary

model

1% 0.87 0.83

3% 0.78 0.73

5% 0.68 0.66


What If My Alphas Have No Risk Factor Bets?

Some managers deliberately strip away risk factor exposures from their alphas

Alpha is completely residual to the factor component of the risk model

What about specific risk?

In an unconstrained case

Does using the same specific risk model promote crowding?

When alphas have no correlation with specific risk, optimization with the standard model has no impact on crowding

More generally, the answer depends on the correlation of different managers’ alphas and specific risk estimates with each other

16

2

1

i

ii

uh

Specific risk


Conclusions

The impact of the risk model on crowding depends on how the alpha signals are constructed

Contrary to a common suspicion, using a standard risk model does not invariably lead to manager crowding

Using a proprietary risk model that incorporates a manager’s alphas may increase or reduce crowding

If the manager’s residual alpha is truly unique, then using a standard risk model in optimization helps differentiate the manager from others, while using a proprietary model may push the manager towards the crowd

17

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Manager Crowding and Portfolio Construction · ©2012. All rights reserved. msci.com msci.com Manager Crowding and Portfolio Construction Do Risk Models Cause Manager Crowding? Jyh-Huei